Question

Find the slope of a line parallel to the given lines

y=-1/3x-7
-y=6x+1

Find the slope of any line perpendicular to the given lines

y=5/2x-1
y=-7x+3

Answer 1

Explanation:

In case of parallel lines, slope is same as that of the given line hence,in first equation ie y=-1/3x-7 slope is -1/3 and in second equation ie -y=6x+1 slope is -6

In case of perpendicular lines,products of slopes is -1.Therefore in first equation ie y=5/2x-1 slope is 5/2 then slope of perpendicular line turns out to be -2/5 and in second equation ie y=-7x+3 slope is -7 then slope of perpendicular line turns out to be 1/7

Answer 2

For the first set of equations:

y = (-1/3)x - 7

The slope of this line is -1/3. Any line parallel to this line will also have a slope of -1/3.

-y = 6x + 1

We can rearrange this equation to be in slope-intercept form:

y = -6x - 1

The slope of this line is -6. Any line parallel to this line will also have a slope of -6.

For the second set of equations:

y = 5/2x - 1

The slope of this line is 5/2. Any line perpendicular to this line will have a slope that is the negative reciprocal of 5/2, which is -2/5.

y = -7x + 3

The slope of this line is -7. Any line perpendicular to this line will have a slope that is the negative reciprocal of -7, which is 1/7.